1. Field of the Invention (Technical Field)
The present invention relates to bearing estimation for accurate location of seismic, acoustic, and other energy transmissive events.
2. Background Art
As the monitoring thresholds of global and regional seismic networks are lowered, bearing estimates become more important to the processes which associate (sparse) detections and which locate events. Current methods of estimating bearings (azimuth from north) from observations by three-component stations (which sense motions in three dimensions simultaneously) and arrays lack both accuracy and precision. Here, accuracy is defined as the precision of the measurement plus the (mean) bias, as may be introduced by a non-homogeneous propagation medium. Precision is the root mean square of the fluctuation in the bearing estimate. Methods are required which will develop all the precision inherently available in the arrival, determine the measurability of the arrival, provide better estimates of the bias induced by non-homogeneous media, permit estimates at low SNRs (signal-to-noise ratios), provide physical insight into the effects of the medium on the estimates, and ultimately produce accurate bearing estimates.
An intelligent estimation process for three-component stations is provided by the present invention. The method, sometimes referred to herein as SEEC (Search, Estimate, Evaluate, and Correct), adaptively exploits all the inherent information in the arrival at every step of the process to achieve optimal results. The approach uses a consistent and robust mathematical framework to define the optimal time-frequency windows on which to make estimates, to make the bearing estimates themselves, to withdraw metrics helpful in choosing the best estimate(s) or admitting that the bearing is immeasurable, and to combine the better estimates on various windows to achieve all the accuracy inherently available. The approach is conceptually superior to current 3 component methods, particularly those that rely on real valued signals, and with minor adjustment is also applicable to estimating bearings on arrays, consisting of many 1, 2 or 3 component receivers.
Other methods of data analysis have been employed which perform polarization analysis of the data, including Vidale, J. E., "Complex Polarization Analysis of Particle Motion", Bull. of the Seismological Soc. of America, Vol. 76, No. 5., pp. 1393-1405 (October 1986); Jurkevics, A., "Polarization Analysis of Three-Component Array Data", Bull of the Seismological Soc. of America, 78, No. 5., pp. 1725-1743 (October 1988); and Lilly, J. M. et al., "Multiwavelet Spectral and Polarization Analysis of Seismic Records", Geophysical Journal International, Vol. 122, pp. 1001-1021 (1995). Jurkevics operates only on real-valued signals, providing azimuths with a standard deviation of about 10.degree. to 12.degree.. Although Jurkevics advocated the use of polarization properties to isolate intervals on which to make bearing estimates, no rationale was offered to isolate the appropriate estimation interval. Indeed, Jurkevics makes a suggestion of using the peak SNR, based on background noise, an approach which fails in practice because it does not account for signal-induced noise. Vidale does not provide bearing estimates. Lilly et al. introduce the use of Slepian wavelets to estimate polarization properties. However, the Slepian wavelets do not adequately minimize bandpass leakage and their work does not address bearing estimates.